To late for the Christmas/New Year parties, but no doubt there will be further opportunities throughout the year for most of us.
My take on this would be…
It all depends on the lighting of course. If you are using available light, then it needs to be reasonable or you will have to have an exposure longer than people can be still for. Using very fast film or a high ISO setting (if digital) will mean you can shorten the exposure.
For exposure of anything slower than about 1/60s you need to have the camera on a steady surface rather than hand-held. A tripod is best but a counter/shelf/wall at the right height will do the job. (A small bean bag or a Joby Gorillapod will give you a lot of options – I use a small Gorillapod with my compact.)
A flash will help. It means you can expose the people close to the camera properly whilst allowing the rest of the night time scene to exposure using ambient light naturally IF your camera gives you this degree of control.
A key challenge is avoiding problems with the flash. This depends on the kind of flash you have and what control you have.
Compact camera on-board flashes for point-and-shoot camera offer you very limited flexibility and it is practically impossible unless you have a model with advanced features to effectively control the two exposures you have that make up a shot when using flash. About the best you achieve is putting some kind of covering over the flash (even toilet paper) to soften it.
If you are using an SLR or DSLR, then you on most models with a built in flash be able to reduce the power of the flash. (Covering still applies.)
Ideally though, you need to use a flash gun. Do not point it directly at the people though. Bounce it off a surface nearby (perhaps a light coloured wall that is behind you). This will provide a very diffused light. This is easier indoors than outdoors of course.
For maximum control, getting the flash gun away from the camera so you have off-axis flash gives you the best results. Diffusion options still apply. Remote requires either a long cable, remote firing components, or a wireless system like that built into Nikon cameras such as the D80 (this is the Nikon Creative Lighting System which lets you use, for example, the small pop-up flash to control one or more remote flash-guns without the pop-up contributing to the exposure itself unless you want it to).
Combining in door ambience with flash is very tricky and something that frankly I rarely make the time to do at parties.